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Shape and discrete sizing optimization of timber trusses by considering of joint flexibility

ADVANCES IN ENGINEERING SOFTWARE 2010年第2期41卷 286-294页

作者： Silih, S. Kravanja, S. Premrov, M. Univ Maribor Fac Civil Engn SLO-2000 Maribor Slovenia

The paper presents the shape and discrete sizing optimization of timber trusses with the consideration of joint flexibility. The optimization was performed by the mixed-integer non-linear programming (MINLP) approach. In the optimization model an economic objective function for minimizing the structure's self-manufacturing costs was defined. The design conditions in accordance with Eurocode 5 were considered as optimization constraints. The internal forces and deflections were calculated by finite element analysis. The structural stiffness matrix was composed by considering fictiously decreased cross-sectional areas of all the flexibly connected elements. The cross-section dimensions and the number of fasteners were defined as discrete sizing variables, while the joint coordinates were considered as shape variables. The applicability of the proposed approach is demonstrated through some numerical examples, presented at the end of the paper. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Discrete sizing optimization Joint flexibility mixed-integer non-linear programming Shape optimization Timber Truss

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integer Quadratic Quasi-polyhedra

Integer Quadratic Quasi-polyhedra

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14th International Conference integer programming and Combinatorial Optimization

作者： Letchford, Adam N. Univ Lancaster Dept Management Sci Lancaster LA1 4YW England

ISBN: (纸本)9783642130359

This paper introduces two fundamental families of 'quasipolyhedra' - polyhedra with a countably infinite number of facets - that arise in the context of integer quadratic programming. It is shown that any integer quadratic program can be reduced to the minimisation of a linear function over a quasi-polyhedron in the first family. Some fundamental properties of the quasi-polyhedra are derived, along with connections to some other well-studied convex sets. Several classes of facet-inducing inequalities are also derived. Finally, extensions to the mixed-integer case are briefly examined.

关键词： mixed-integer non-linear programming polyhedral combinatorics convex analysis

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Branching and bounds tightening techniques for non-convex MINLP

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OPTIMIZATION METHODS & SOFTWARE 2009年第4-5期24卷 597-634页

作者： Belotti, Pietro Lee, Jon Liberti, Leo Margot, Francois Waechter, Andreas Lehigh Univ Dept Ind & Syst Engn Bethlehem PA 18015 USA IBM Corp TJ Watson Res Ctr Yorktown Hts NY USA Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA Ecole Polytech LIX F-91128 Palaiseau France

Many industrial problems can be naturally formulated using mixed integer non-linear programming (MINLP) models and can be solved by spatial BranchBound (sBB) techniques. We study the impact of two important parts of sBB methods: bounds tightening (BT) and branching strategies. We extend a branching technique originally developed for MILP, reliability branching, to the MINLP case. Motivated by the demand for open-source solvers for real-world MINLP problems, we have developed an sBB software package named couenne (Convex Over- and Under-ENvelopes for non-linear Estimation) and used it for extensive tests on several combinations of BT and branching techniques on a set of publicly available and real-world MINLP instances. We also compare the performance of couenne with a state-of-the-art MINLP solver.

关键词： mixed-integer non-linear programming Couenne branching rules bounds tightening

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Power-flow Model of Sen Transformer for Loadability Enhancement and Comparison with Unified Power-flow Controllers in Hybrid Electricity Markets

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2009年第2期37卷 189-209页

作者： Kumar, Ashwani Gao, Wenzhong Tennessee Technol Univ Ctr Energy Syst & Res Dept Elect & Comp Engn Cookeville TN 38505 USA

This article proposes a power-flow model of Sen transformer and a mixed-integer-based non-linear programming approach for its optimal location in competitive electricity markets. The system loadability has been determined for a pool, as well as hybrid electricity market, model incorporating an AC load flow-based secure bilateral transaction matrix in an optimal power-flow model. The results have also been obtained with optimally placed unified power-flow controllers and thyristor-controlled series capacitors for comparison. The proposed technique has been demonstrated on the IEEE 24-bus reliability test system.

关键词： optimal power flow secure transaction matrix mixed-integer non-linear programming flexible AC transmission system controllers competitive electricity market

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Technology adoption decisions under a mixed regulatory system of tradable permits and air pollution fees for the control of total suspended particulates in Taiwan

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Journal of Regulatory Economics 2009年第2期35卷 135-153页

作者： Liao, Chao-Ning Department of Economics National Cheng-Kung University Tainan Taiwan

By using a newly proposed tradable permit system built under the current air pollution fee regulation for the control of Total Suspended Particulates in Taiwan as an example, a mixed-integer non-linear programming model that minimizes the total regulatory costs of firms is applied to investigate how different permit trading ratios and the design of banking might affect firms' technology adoption decisions and permit trading behavior. By incorporating binary variables in the model to represent firms' decisions as to whether or not to install new control equipment, the results show that when the unit air pollution fee rate is higher than the firms' abatement costs, the design of banking causes many firms to install new control equipment that results in an over-reduction of emissions. If no air pollution fee is imposed, the trading ratio plays a more important role than the reservation rate for banking in determining the firms' emission reduction strategies under a pure permit trading scheme. While the conclusion from this study that uses a non-uniformly mixed pollutant as an example may hold only when certain conditions are met, the framework can be applied to other uniformly mixed pollutants through parameter changes without any limitation. In addition, the modeling technique presented here offers policy-makers a very convenient approach to empirical analysis. © 2008 Springer Science+Business Media, LLC.

关键词： Air pollution fee Banking mixed-integer non-linear programming Total Suspended Particulates Tradable permits

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Comparison of Sen Transformer and Unified Power Flow Controller on Spot Price Variation of Real and Reactive Power under Maximum Loadability Condition

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2008年第12期36卷 1369-1387页

作者： Chanana, Saurabh Kumar, Ashwani Natl Inst Technol Dept Elect Engn Kurukshetra 136119 Haryana India

In competitive electricity markets, the locational marginal price, or spot price, of power has become an important indicator of competitiveness and market efficiency. System operators throughout the world utilize the locational marginal price of active power for congestion management, auctioning of transmission rights, and pricing of transmission service. Recent studies have indicated the locational marginal price of reactive power has a role to play in improving system reliability and pricing voltage support services. In this article, a study of variation in locational marginal price of active and reactive power under normal and maximum loadability conditions has been carried out. A two-step optimization problem of maximizing system loadability and social welfare is proposed. Recently, there has been considerable interest in the role of power flow controllers in competitive electricity markets. In this article, a comparative study of impact of power flow control devices, such as the unified power flow controller and Sen transformer, on locational marginal prices of active and reactive power under maximum loadability condition has been carried out. The placement of these power flow control devices in a system has been obtained using mixed-integer non-linear programming. The study has been conducted on two IEEE test systems14- and 57-busfor a pool market model.

关键词： loadability factor locational marginal price mixed-integer non-linear programming Sen transformer unified power flow controller

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A hybrid approach toward security-constrained reactive power planning in electricity markets

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2008年第6期36卷 649-663页

作者： Parida, S. K. Singh, S. N. Srivastava, S. C. Indian Inst Technol Kanpur 208016 Uttaranchal India

In this article, a hybrid approach for reactive power planning has been proposed that makes use of both numerical and analytical methods. Optimal power flow formulations with four different objectives have been solved for a system-intact and for a few severe contingency cases with the help of mixed-integer non-linear programming. For each objective, ranking of optimal bus locations for reactive power sources have been obtained. The results, so obtained, have been used to arrive at an overall performance sensitivity factor for locating reactive power sources employing an analytic hierarchical process algorithm. The proposed method for reactive power planning has been demonstrated on a IEEE 24-bus reliability test system.

关键词： reactive power planning optimal power flow mixed-integer non-linear programming analytic hierarchical process

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The two-phase MINLP optimization of a single-storey industrial steel building

The two-phase MINLP optimization of a single-storey industri...

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4th International Conference on High Performance Structures and Materials

作者： Zula, T. Kravanja, S. Univ Maribor Fac Civil Engn SLO-2000 Maribor Slovenia

ISBN: (纸本)9781845641061

The paper presents the two-phase MINLP topology and standard sizes optimization of a single-storey industrial steel building. The structure consists of main portal frames, connected with purlins. It is made from standard hot rolled I sections. The mixed-integer non-linear programming (MINLP) optimization of the structure is applied. The MINLP performs a discrete topology and standard dimension optimization, while continuous parameters (stresses, deflections, mass, costs, etc.) are calculated simultaneously inside, the continuous space. Since the discrete/continuous optimization problem of this type of structures is non-convex and highly non-linear, the Modified Outer-Approximation/Equality-Relaxation (OVER) algorithm is used for the optimization. The defined mass objective function is subjected to the set of equality and inequality constraints known from the structural analysis and dimensioning. The dimensioning of steel members is performed in accordance with Eurocode 3. The MINLP optimization is performed in two phases. In the first phase, the topology optimization of the structure at the relaxed dimensions is performed only. This phase gives a good linear global approximation to the structure for the next phase. When the optimal topology is reached, the optimization is continued at the second phase for the overall topology and standard section discrete optimization. Alongside the optimal structure mass, the optimal topology with the optimal number of portal frames and purlins as well as all standard cross-sections are obtained. The paper includes the theoretical basis and a practical example with the results of the optimization.

关键词： optimization topology optimization discrete sizes optimization mixed-integer non-linear programming MINLP industrial steel building

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Computational implementation of non-linear convex hull reformulation

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COMPUTERS & CHEMICAL ENGINEERING 2007年第7期31卷 856-866页

作者： Sawaya, Nicolas W. Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

Lee and Grossmann [Lee, S., & Grossmann, I. E. (2000). New algorithms for nonlinear generalized disjunctive programming. Computers and Chemical Engineering, 24, 2125-2141] have developed a reformulation for nonlinear Generalized Disjunctive programming (GDP) problems that obtains from the intersection of the convex hulls of every disjunction. In order to computationally implement this method, it is necessary to reformulate the problem in such a way so as to avoid division by zero in the nonlinear inequalities present amongst the convex bull constraints, while preserving the convex nature of the problem. To accomplish this, we propose to replace the original set of nonlinear constraints by two different sets of convex constraints that circumvent the aforementioned problem and that approximate the original set of constraints exactly at their limit. Furthermore, we compare the two sets of approximating constraints against each other and give rigorous theoretical conditions under which one is superior to the other. Finally, we illustrate the efficiency of both approximations on a variety of numerical examples draw from the Chemical Engineering and Operations Research literature. (C) 2006 Elsevier Ltd. All rights reserved.

关键词： disjunctive programming convex hull mixed-integer non-linear programming

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Modelling a mixed system of air pollution fee and tradable permits for controlling nitrogen oxide: a case study of Taiwan

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AUSTRALIAN JOURNAL OF AGRICULTURAL AND RESOURCE ECONOMICS 2007年第4期51卷 475-490页

作者： Liao, Chao-Ning Natl Cheng Kung Univ Dept Econ Tainan 701 Taiwan

A mixed-integer non-linear programming model that minimises the total regulatory costs of controlling nitrogen oxide is used to investigate how a newly proposed permit trading scheme in Taiwan, which incorporates the features of banking and a non-one-to-one trading ratio, may affect firms' emission reduction strategies and permit trading decisions. Compared to the previous regulation where only an air pollution fee is used, the new regulation that requires a reduction in emissions by 10 per cent from the emission level in the year 2000 for a 5 year period will increase the costs by 77 per cent, which is equivalent to US$9.87 million. The design of banking and the increasing returns to scale characteristic of pollution control among firms might lead to an uneven reduction in emissions in each year. Setting a lower reservation rate for banking would, however, help maintain a more stable environmental quality without a significant loss to the government in terms of air pollution fee revenue.

关键词： air pollution fee banking mixed-integer non-linear programming nitrogen oxide tradable permits

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